If you bet on "red" at roulette, you have chance 18/38 of winning. Suppose you make a sequence of independent bets on “red” at roulette, with the decision that you will stop playing once you have won 5 times. What is the chance that after 15 bets you are still playing?
We use [binomial] probability mass function. To calculate the probability, you have to estimate the probability of having up to 4 successful bets after the 15th. So the final probability will be the sum of the probability to get 0 successful bets in 15 bets, plus the probability to get 1 successful bet, ..., to the probability of having 4 successful bets in 15 bets.
To achieve it:
import scipy.stats as ss n = 15 # Number of total bets p = 18./38 # Probability of getting "red" at the roulette